Fast Point Multiplication on Elliptic Curves without Precomputation

Elliptic curves find numerous applications. This paper describes a simple strategy to speed up their arithmetic in right-to-left methods. In certain settings, this leads to a non-negligible performance increase compared to the left-to-right counterparts.

[1]  Henri Cohen,et al.  A course in computational algebraic number theory , 1993, Graduate texts in mathematics.

[2]  Marc Joye,et al.  Low-cost solutions for preventing simple side-channel analysis: side-channel atomicity , 2004, IEEE Transactions on Computers.

[3]  Daniel M. Gordon,et al.  A Survey of Fast Exponentiation Methods , 1998, J. Algorithms.

[4]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[5]  Frédéric Valette,et al.  The Doubling Attack - Why Upwards Is Better than Downwards , 2003, CHES.

[6]  Kazuo Ohta,et al.  Advances in Cryptology — ASIACRYPT’98 , 2002, Lecture Notes in Computer Science.

[7]  Paul C. Kocher,et al.  Differential Power Analysis , 1999, CRYPTO.

[8]  Michael Wiener,et al.  Advances in Cryptology — CRYPTO’ 99 , 1999 .

[9]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[10]  J. Olivos,et al.  Speeding up the computations on an elliptic curve using addition-subtraction chains , 1990, RAIRO Theor. Informatics Appl..

[11]  Christof Paar,et al.  Cryptographic Hardware and Embedded Systems - CHES 2003 , 2003, Lecture Notes in Computer Science.

[12]  Joseph H. Silverman,et al.  The arithmetic of elliptic curves , 1986, Graduate texts in mathematics.

[13]  Ricardo Dahab,et al.  Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation , 1999, CHES.

[14]  Donald Ervin Knuth,et al.  The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information , 1978 .

[15]  D. Chudnovsky,et al.  Sequences of numbers generated by addition in formal groups and new primality and factorization tests , 1986 .

[16]  W. Neville Holmes,et al.  Binary Arithmetic , 2007, Computer.

[17]  Atsuko Miyaji,et al.  Efficient Elliptic Curve Exponentiation Using Mixed Coordinates , 1998, ASIACRYPT.

[18]  M. D. MacLaren The Art of Computer Programming. Volume 2: Seminumerical Algorithms (Donald E. Knuth) , 1970 .

[19]  P. L. Montgomery Speeding the Pollard and elliptic curve methods of factorization , 1987 .